Finite Group DatabasebetaFinite Group Databasebeta| order | 16182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D29×C31⋊C9 |
| unambiguous semidirect product | C29⋊(C2×C31⋊C9) |
| unambiguous semidirect product | (C31×D29)⋊C9 |
| derived, Hall | C29×C31 ⋊ C2×C9 |
| Hall | C29×C31⋊C9 ⋊ C2 |
| Hall | C31×D29 ⋊ C9 |
| Sylow | C31 ⋊ C9×D29 |
| Sylow | C29 ⋊ C2×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D29×C31⋊C3 |
| commutator, hypocenter | C29×C31 | C2×C9 |
| Fitting, socle, cosocle | C3×C29×C31 | C2×C3 |
| prime radical | C3×C31×D29 | C3 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8091 |
624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C31⋊C9)⋊#1181, #1181×C31⋊C9, D29×D31⋊C9, … |
| maximal normal subgroup of | (C31⋊C9)⋊#1181, #1181×C31⋊C9, D29×D31⋊C9, … |
| maximal quotient of | Dic29×C31⋊C9, C2×D29×C31⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16182, 11);